Based on these observations, we formulate a learning framework for PDFA where the teacher's answers to \(\mathbf {MQ}\)  are probability distributions over the symbols a string could be continued with. These are called next-symbol probability distributions. Besides, in the case the learner is allowed to produce hypotheses whose next-symbol probability distributions are approximations of the target ones, we propose to resort to quantization as an abstraction which allows us to define a coarser equivalence relation than the latter. This ensures the learnt automaton to be equivalent to the target one modulo this relation.
Finally, we propose and implement \(\mathrm {QuaNT}\) , a learning algorithm for PDFA that uses an adaptation of the tree structure of [1]}. In order to assess its performance, we compared \(\mathrm {QuaNT}\)  to a clustering-based algorithm that uses an observation table and a tolerance-based non-equivalence similarity relation, similar to \(\mathrm {WL}^\ast \) .
The experiments carried out showed that \(\mathrm {QuaNT}\)  was orders of magnitude more efficient.
